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Unformatted text preview: Stat 210B Homework Assignment 5 (due April 3) 1. Suppose Pn − Qn → 0. Show that Pn and Qn are mutually contiguous. 2. Suppose, under Pn , Xn = Yn + oPn (1). Suppose Qn is contiguous to Pn . Show that Xn = Yn + oQn (1).
n 3. Suppose Pθ is the uniform distribution on (0, θ). Let Pθ denote the distribution of n iid n and P n draws from Pθ . Fix h and determine whether or not P1 1+h/n are mutually contiguous. Consider both h > 0 and h < 0. 4. Let X1 , . . . , Xn be a random sample from a density f (x − θ) where f is symmetric about zero. Calculate the relative eﬃciency of the ttest and the test that rejects for large values of i<j 1{Xi + Xj > 0} for f equal to the logistic, normal, Laplace and uniform shapes. 5. Problem 14.9 in van der Vaart. ...
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This note was uploaded on 01/25/2011 for the course STAT 201b taught by Professor Michaeljordan during the Fall '05 term at University of California, Berkeley.
 Fall '05
 MICHAELJORDAN
 Probability

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